_{}
is used here to denote the fraction of *a* over *b*. *a* is called the numerator and *b* is called the denominator and must be non zero.

Examples of fractions: _{}

NOTE:
_{}
is undefined since division by zero is undefined in mathematics.

A calculator to add fractions is included in this website. You may use it to check your answers.

How to add fractions?

## 1. Add fractions with equal denominator

__Example 1:__ Add and simplfy.

__Solution to Example 1__

To add fractions with the same denominator, you add the __numerators__, keep the same denominator and simplify if possible

__Example 2:__ Add, simplify and express the final answer as a fraction.

__Solution to Example 2__

Add the numerators

## 2. Add fractions with non equal denominators

__Example 3:__ Add, simplify and express the final answer as a fraction.

__Solution to Example 3__

We first need to find the lowest common multiple (LCM) of the denominators 9 and 6 by factoring into prime factors.

We next convert the two given fractions so that they have common denominator equal to the LCM = 18. The denominator of the fraction _{} is 9 and we need to multiply numerator and denominator by 2 in order to change the denominator to 18

The denominator of the fraction _{} is 6 and we need to multiply numerator and denominator by 3 in order to change the denominator to 18

Now that we have converted the two fractions so that they have common denominator, we can easily add them as follows

__Example 4:__ Add, simplify and express the final answer as a fraction and as a mixed number.

__Solution to Example 4__

Find the LCM of the denominators 15 and 55

We convert the given fractions so the they have common denominator equal to the LCM = 165. The denominator of the fraction
_{} is 15 and both numerator and denominator need to be multiplied by 11 in order to change the denominator to 165

The second fraction _{} is converted to one with the denominator equal to 165 by multiplying numerator and denominator by 3 in order to change the denominator to 165

We now add the fractions

__Example 5:__ Add, simplify and express the final answer as a fraction.

__Solution to Example 5__

We first convert 2 into a fraction

The common denominator will be 5

We now add

__Exercises:__ Add, simplify and express the answer as a fraction and as a mixed number.

__Answers to Above Exercises:__.

More on fractions
and fraction calculators.